An iterative rate-distortion optimization algorithm for MPEG I/II Layer-3 (MP3) encoding based on the method of Lagrangian multipliers. Generally, an iterative method is performed such that a global quantization step size is determined while scale factors are fixed, and thereafter the scale factors are determined while the global quantization step size is fixed. This is repeated until a calculated rate-distortion cost is within a predetermined threshold. The methods are demonstrated to be computationally efficient and the resulting bit stream is fully standard compatible.